Finding a change in a variable due to a change in another variable

I want to write a code for finding potential temperature. There I want to fix temperature. And at that temperature level, I want to calculate potential temperature varying the pressure. Then for different temperatures, I want to repeat the process. For more info about potential temperature, check this-Potential temperature. But the problem with temperature is that I can't just pick any arbitrary interval or change in temperature value. In atmosphere, there is a term called lapse rate. There temperature changes in a certain manner, i.e 6.5K/100hPa. I want to implement this change in my temperature range, How can I do this? I have chosen 300K as the base temperature and 1010hPa as base pressure.

p=200:1000;
t=210:305;

for i=1:length(t)
    for j=1:length(p)
        theta(i,j)=t(i)*((1000/p(j))^0.286);
    end
end

figure 
contourf(t,p,theta')
set(gca,'YDir','reverse')

[Jan]

Remember that for Matlab and the readers the values are just number. Therefor the term "temperatur" is confusing only.

Find the formula you want to implement. Afterwards this is a question concerning Matlab. Currently you did not explain, what you want to impelement, only that it is something.

[Anirban Mandal]

I have explained above what I want to do. If you go throught the code you can understand my intention.

Answer 1

[Star Strider]

See if the griddedInterpolant function will produce the desired result

p=200:1000;
t=210:305;
[P,T] = ndgrid(p,t);
Z = T.*((1000./P).^0.286);
PT = griddedInterpolant(P,T,Z);

P760_T273 = PT(760,273)                 % Potential Temperature At P=760 & T=273

P760_T273 = 295.2908

EDIT — (11 Nov 2021 at 13:04)

An anonymous function would also work —

PTfcn  = @(P,T) T.*((1000./P).^0.286);
P760_T273f = PTfcn(760,273)

P760_T273f = 295.2908

.

[Anirban Mandal]

Thanks. I figured out another way though. Since temperature is decreasing in a certain way, I initiated a loop where I defined the decrease in temperature. Then I used those temperature values in the next loops for calculating theta.

[Star Strider]

As always, my pleasure!

I admit that I was not absolutely certain what the desired result was. (A similar relation, important in aviation, is Density altitude.)

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